A: Both FEBI and Feldenkrais connect body and mind, so in that sense they are similar, and I can see why your client would ask this question. Both attend deeply to how the body is functioning. The FEBI is measuring large-scale patterns functioning throughout the nervous system. Indeed, the theory is that when one part of the body-mind goes into a pattern, the rest tends to follow. That's why changing how we move changes how we think.
I would refine the theory to add that our ENTIRE mind-body doesn't necessarily get there. We still carry residual tension and our home pattern is still functioning in the background (i.e., when we try to relax, our entire body doesn't relax all at once). Where Feldenkrais focuses is on this very point: we tend to habitually tense and link muscle movements together that aren't needed for the most efficient movement. For example, raising our eyebrows when we open our mouth to take a spoonful of soup. Or raising our shoulders when we lift a book. Even when we try to relax our movement, some parts don't relax. We have to consciously go into a movement, tease apart what's essential from what's unnecessary and re-learn the most efficient movement. That's what Feldenkrais techniques teach one to do. Paired with an understanding of the patterns and FEBI, people who practice Feldenkrais will get a better sense of where they habitually hold tension, and which pattern centers are activated and essential for which physical movements.